Interpretive Summary: Dust particles blown from the surface of the earth during a wind erosion event eventually settle back to earth at a rate that depends upon many factors. Particle size, density, shape and external factors such as air density, viscosity, and the local gravitational field strength appreciably affect the fall velocity of particles. Another important factor is the level of atmospheric turbulence. Submicron size particles can be suspended indefinitely as they are swept along by swirling eddies in turbulent flow. Larger particles, however, fall through the fluid and experience forces that result from this relative motion. Particles that are of sufficient size experience a drag force that is a nonlinear function of the relative velocity between the particle and fluid. The primary goal of this work is to explore the effects of nonlinear drag on the settling velocity of particles by calculating their motion while falling through moving fluids. The prediction of particle motion is based upon equations that predict the natural reaction of particles to applied fluid dynamic and gravitational forces. We find that nonlinear drag produces a substantial reduction of the settling velocity of falling particles in turbulent flows and in simple oscillating fluids. Particles that fall more slowly are carried greater distances by wind.

Technical Abstract:
The effect of nonlinear drag on the motion and settling velocity of heavy particles in a turbulent atmosphere is investigated. We approach the problem rather systematically by first considering the response of particles to much simpler fluid motions that are subprocesses of the more complex turbulent field. We first consider the motion and time response of particles falling under gravity in still fluid. Then we investigate the effects of a sudden gust or step change in relative velocity between a falling particle and its surrounding fluid. We demonstrate that horizontal relative motion produced by a sudden gust tends to reduce the settling velocity of a particle. In simple oscillating fluids we show that the reduction of settling velocity increases with increasing amplitude of fluid oscillation. We also explore the effects of oscillation frequency on the settling velocity and show that, if the period of fluid oscillation is less than the particle response time, then the settling velocity reduction becomes independent of oscillation frequency. Finally, we explore the motion of heavy particles within simulated isotropic turbulence and show that the effect of nonlinear drag is to produce a slowing of particle settling velocity